Eur. Phys. J. C 70, 1119-1130 (2010)
https://doi.org/10.1140/epjc/s10052-010-1487-z

Bosonic colored group field theory

¹ Laboratoire de Physique Théorique, Université Paris XI, 91405, Orsay Cedex, France
² Centre de Physique Théorique, Ecole Polytechnique, 91128, Palaiseau Cedex, France
³ International Chair in Mathematical Physics and Applications (ICMPA–UNESCO Chair), University of Abomey–Calavi, 072 B.P. 50, Cotonou, Republic of Benin
⁴ Département de Mathématiques et Informatique, Faculté des Sciences et Techniques, Université Cheikh Anta Diop, Dakar, Senegal

jobengeloun@gmail.com

Received: 9 November 2009
Revised: 17 September 2010
Published online: 19 November 2010

Abstract

Bosonic colored group field theory is considered. Focusing first on dimension four, namely the colored Ooguri group field model, the main properties of Feynman graphs are studied. This leads to a theorem on optimal perturbative bounds of Feynman amplitudes in the “ultraspin” (large spin) limit. The results are generalized in any dimension. Finally, integrating out two colors we write a new representation, which could be useful for the constructive analysis of this type of models.